Saturday, March 06, 2010

Symmetry / Simetria (5)

Cuboctahedron (1) puzzle
In each of these photos one can see one of over an hundred natural solutions of the cuboctahedron (1) puzzle. They are taken in such a way that one can see it is symmetric by a reflection (here colours do not matter, only numbers matter). The "mirror" is in the middle of the photo. This is a symmetry of this solution. This symmetry belongs to the group of this solution. If you exchange (make a permutation) of the numbers you obtain the same natural solution that belongs also to its group. It is the cube's group and it has 48 elements. We just saw a simple way of showing an isomorphism between the cube's group and the group generated by the reflections and the permutations of {1,2,3,4}: {-1,1}xS4.

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